Trait-QTL-heritability of grain yield and other agronomic traits under low nitrogen conditions in bi-parental maize populations

Limited or low Nitrogen is a wanting abiotic stress in maize mainly in Sub-Sahara Africa, affecting yields and quality development of maize crop. As an approach to getting a breeding solution; mapping of QTLs and understanding the heritability factor can provide useful information and guide for breeders in developing low nitrogen resilient maize. QTL mapping which is a molecular breeding component forms an actual basis in estimation of genomic regions associated to the expression of quantitative traits, and how heritable are such traits. Conducting a selection for Low N-tolerance is challenging due to its complex nature with strong interaction between genotypes and environments; therefore, marker assisted breeding is key to improving such complex traits, but at the same time requires markers associated with the trait of interest. In this study, three bi-parental populations were subjected to either or both low and optimum N conditions to detect and determine the QTLs heritability for grain yield and other agronomic traits. Essential to the study; genotype by environmental interaction, significance and heritability was examined for each population with most traits expressing low (<0.2) and moderate to high heritabilities (0.3>). These QTLs with high heritabilities across environments will be of great value for rapid introgression into maize populations using marker assisted selection approach. The study was a preliminary and therefore require further validation on heritability and fine mapping for them to be useful in MAS.

S-derivative of perturbed mapping and solution mapping for parametric vector equilibrium problems

In this paper, we deal with the sensitivity analysis in vector equilibrium problems by using the S-derivative of a set-valued mapping. We first investigate the S-derivative on a kind of set-valued gap function for the vector equilibrium problems. Based on these results, S-derivative estimations on a perturbed mapping for the parametric vector equilibrium problem are given. Moreover, we provide some examples to illustrate the obtained results. Finally, we derive the S-derivative estimations of a solutions mapping of the parametric vector equilibrium problems via S-derivative estimations of a kind of the parametric variational system.

Explicit and Implicit Non-convex Sweeping Processes in the Space of Absolutely Continuous Functions

We show that sweeping processes with possibly non-convex prox-regular constraints generate a strongly continuous input-output mapping in the space of absolutely continuous functions. Under additional smoothness assumptions on the constraint we prove the local Lipschitz continuity of the input-output mapping. Using the Banach contraction principle, we subsequently prove that also the solution mapping associated with the state-dependent problem is locally Lipschitz continuous.

The second-order composed radial derivatives of perturbation mappings of parametric set-valued optimization problems

In the paper, we study the generalized differentiability in set-valued optimization, namely stydying the second-order composed radial derivative of a given set-valued mapping. Inspired by the adjacent cone and the higher-order radial con in Anh NLH et al. (2011), we introduce the second-order composed radial derivative. Then, its basic properties are investigated and relationships between the second-order compsoed radial derivative of a given set-valued mapping and that of its profile are obtained. Finally, applications of this derivative to sensitivity analysis are studied. In detail, we work on a parametrized set-valued optimization problem concerning Pareto solutions. Based on the above-mentioned results, we find out sensitivity analysis for Pareto solution mapping of the problem. More precisely, we establish the second-order composed radial derivative for the perturbation mapping (here, the perturbation means the Pareto solution mapping concerning some parameter). Some examples are given to illustrate our results. The obtained results are new and improve the existing ones in the literature.

Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory

In the present article, we consider a von Kárman equation with long memory. The goal is to study a quadratic cost minimax optimal control problems for the control system governed by the equation. First, we show that the solution map is continuous under a weak assumption on the data. Then, we formulate the minimax optimal control problem. We show the first and twice Fréchet differentiabilities of the nonlinear solution map from a bilinear input term to the weak solution of the equation. With the Fréchet differentiabilities of the control to solution mapping, we prove the uniqueness and existence of an optimal pair and find its necessary optimality condition.